#### Question

The diameter of a wheel of a bus is 90 cm which makes 315 revolutions per minute. Determine its speed in kilometres per hour. [Use π = 22/7]

#### Solution

It is given that the diameter of the wheel is 90 cm.

∴ Radius of the circular wheel, r \[= \frac{90}{2} = 45 cm . \]

∴ Perimeter of the wheel \[= 2 \times \pi \times r = 2 \times \frac{22}{7} \times 45 = 282 . 857 cm\]

It means the wheel travels 282 . 857 cm in a revolution.

Now, it makes 315 revolutions per minute.

∴ Distance travelled by the wheel in one minute \[= 315 \times 282 . 857 = 89100 cm\]

∴ Speed = 89100 cm per minute \[= \frac{89100 cm}{1 \text{ minute }}\]

Now, we need to convert it into kilometers per hour.

\[ \therefore \frac{89100 cm}{1\text{ minute }} = \frac{89100 \times \frac{1}{100000}\text{ kilometer }}{\frac{1}{60}\text{ hour }}\]

\[ = \frac{89100}{100000} \times \frac{60}{1} \times \frac{\text{ kilometer }}{\text{ hour }}\]

= 53 . 46 kilometers per hour